The present invention is directed to devices for Fourier transformation. Specifically, it relates to the generation of a three-dimensional Fourier transform, the three dimensions being time and two spatial dimensions.
Devices for rapidly locating and identifying the source of an electromagnetic signal often employ Fourier transformation from time to temporal frequency and from position to spatial frequency. The reason for the transformation from time to temporal frequency is obvious: the frequency of the signal is often the single most important factor in identifying the source. Transformation in spatial frequency also turns out to be important. If the signals from a linear array of antenna elements are sampled simultaneously, the resultant group of values has a spatial frequency that is a function of the direction of the source and the temporal frequency of the signal. If the frequency of the source is known--which it is if the Fourier transformation from time to temporal frequency is performed--then the direction of the source can be determined from the ratio of spatial frequency to temporal frequency.
An elegant means for generating a two-dimensional Fourier transform in time and one spatial dimension is the two-dimensional compressive receiver. This device includes a two-dimensional delay line that has input ports arrayed along one end and output ports arrayed along its other end. The delay line is dispersive, having a linear relationship between delay and input-signal frequency. The signals on the antenna elements caused by a source are translated in frequency by frequency translators associated with the elements. The amount of translation sweeps repetitively at a rate that corresponds to the linear frequency-delay relationship of the delay line. The outputs of the frequency translators are applied to the input ports of the two-dimensional delay line. Because of the frequency sweep, later-launched delay-line signals caused by a given frequency component at the frequency-translator input ports travel faster than earlier-launched signals caused by the same frequency component, and the difference in velocity is such that all delay-line signals resulting from a given frequency component in the translator inputs during a given sweep arrive at the output end of the delay line at substantially the same time; i.e., the frequency component is "compressed" in time. Other frequency components are also compressed, but the compressed results of different frequency components arrive at the output end at different times. Hence, the compressive receiver performs a Fourier transformation from the time domain to the temporal-frequency domain.
It also performs a transformation from the position domain to the spatial-frequency domain. The two-dimensional delay line is configured for constructive interference at the output end of the delay line if the signals at the input ports are delayed versions of each other and if their delays bear a linear relationship to position along the input edge. The position on the output end at which the constructive interference occurs depends on the spatial frequency of the group of signals at the input ports. For instance, if all the signals arrive at the same time, there is no advance in phase along the input edge, so the spatial frequency is zero, and the constructive interference occurs near the middle of the output edge. On the other hand, if the input signal has a high temporal frequency and there is a relatively long delay between the various input ports, then there is a large phase advance across the input edge. Therefore, constructive interference occurs toward one or the other side of the output end. There is thus a transformation from position to spatial frequency.
This type of arrangement can be used as a powerful monitoring tool. If the inputs to the frequency translators are signals from elements in a linear antenna array, the time at which an output from the delay line occurs is an indication of the frequency at which the source is radiating. Once the temporal frequency is known, the direction of the source is readily determined from the position of the output port at which the signal occurs. With appropriate modifications, the compressive receiver can also be used with non-linear antenna arrays.
The two-dimensional compressive receiver can thus give information concerning temporal frequency and, say, the azimuth angle of the source. In the alternative, it can be used to determine elevation and temporal frequency. Clearly, however, the same two-dimensional compressive receiver cannot be employed to indicate frequency, azimuth, and elevation simultaneously. Furthermore, although one can use two two-dimensional compressive receivers with orthogonal linear arrays to determine azimuth, elevation, and frequency, ambiguity in position can result if signals from two sources are at the same frequency.
It is thus an object of the present invention to apply the principles of the compressive receiver to three dimensions. It is a further object to provide for unambiguous determination of azimuth, elevation, and frequency simultaneously.